From a solid cylindrical wooden block of height 18 cm and radius 7.5 cm, a conical cavity of the same height and same radius is taken out. What is total surface area (in cm2) of the remaining solid?

Answer: Option D

Solution

Answer: Option D

Solution:

$$\begin{array}{rl}& l^2=r^2+h^2\\ & l^2={\left(7.5\right)}^2+{\left(18\right)}^2\\ & l^2=\frac{225}{4}+324\\ & l^2=\frac{1521}{4}\\ & l=\frac{39}{2}\\ & \text{Total surface area}=\pi rl+2\pi rh+\pi r^2\\ & =\pi r\left[l+2h+r\right]\\ & =\pi \times \frac{15}{2}\left[\frac{39}{2}+36+\frac{15}{2}\right]\\ & =\pi \times \frac{15}{2}\left[\frac{126\times 15}{2}\right]\\ & =\left[\frac{945}{2}\right]\pi \\ & =472.5\pi \end{array}$$